Professor Emeritus
Laboratory for Advanced Computing
Laboratory for Control and Information
Department of Mathematics, Statistics, and Computer Science
University of Illinois at Chicago
Annotated Publications in
Computational Finance and Bioeconomics
(Most recent papers have preprint links.)
30[NRM88]. F. B. Hanson and D. Ryan, Optimal harvesting with density dependent random effects, Natural Resource Modeling, vol. 2, pp. 439-455, 1988.
64 [MBS98]. F. B. Hanson and D. Ryan, " Optimal Harvesting with Both Population and Price Dynamics," Mathematical BioSciences, vol. 148, issue 2, pp. 129-146, March 1998.
76 [ACC01]. F. B. Hanson and J. J. Westman, " Optimal Consumption and Portfolio Policies for Important Jump Events: Modeling and Computational Considerations ," Proceedings of 2001 American Control Conference, pp.4456-4661, 25 June 2001.
78 [ACC02]. F. B. Hanson and J. J. Westman, " Optimal Consumption and Portfolio Control for Jump-Diffusion Stock Process with Log-Normal Jumps (corrected) ," Proceedings of 2002 American Control Conference, pp. 4256-4261 (1573-1578), 08 May 2002.
80 [KU02FM]. Floyd B. Hanson and John J. Westman, " Stochastic Analysis of Jump-Diffusions for Financial Log-Return Processes (corrected)," in Stochastic Theory and Control, Proceedings of a Workshop held in Lawrence, Kansas, October 18-20, 2001, Lecture Notes in Control and Information Sciences, B.Pasik-Duncan (Editor), Springer-Verlag, New York, pp. 169-184, 24 July 2002.
83 [MTMS02FM2]. F. B. Hanson and J. J. Westman, " Computational Methods for Portfolio and Consumption Optimization in Log-Normal Diffusion, Log-Uniform Jump Environments," Proceedings of the 15th International Symposium on Mathematical Theory of Networks and Systems, 9 pages, 12 August 2002 (invited paper).
84 [MTMS02FM1]. F. B. Hanson and J. J. Westman, " Jump-Diffusion Stock Return Models in Finance: Stochastic Process Density with Uniform-Jump Amplitude," Proceedings of the 15th International Symposium on Mathematical Theory of Networks and Systems, 7 pages, 12 August 2002 (invited paper).
85 [CDC02]. F. B. Hanson and J. J. Westman, " Portfolio Optimization with Jump--Diffusions: Estimation of Time-Dependent Parameters and Application," Proceedings of 2002 Conference on Decision and Control, pp. 377-382, 09-13 December 2002, invited paper CDC02-INV0302.
87 [ACC03]. F. B. Hanson and J. J. Westman, " Jump--Diffusion Stock-Return Model with Weighted Fitting of Time-Dependent Parameters," Proceedings of 2003 American Control Conference, pp. 4869-4874, 04 June 2003.
89 [TAC04]. Floyd B. Hanson and John J. Westman, "Optimal Portfolio and Consumption Policies Subject to Rishel's Important Jump Events Model: Computational Methods," Trans. Automatic Control, vol. 49, no. 3, Special Issue on Stochastic Control Methods in Financial Engineering, pp. 326-337, March 2004.
91 [CM04].
Floyd B. Hanson, John J. Westman and Zongwu Zhu,
"
Maximum Multinomial Likelihood Estimation of Market Parameters
for Stock Jump-Diffusion Models,
in Mathematics of Finance: Proc. 2003 AMS-IMS-SIAM Joint Summer Research
Conference on Mathematics of Finance, AMS Contemporary
Mathematics
G. Yin and Q. Zhang (Editors),vol. 351, pp.~155-169, 24 June 2004.
92 [CDC04].
Floyd B. Hanson
and
Zongwu Zhu,
"
Comparison of Market Parameters for Jump-Diffusion Distributions
Using Multinomial Maximum Likelihood Estimation,
Proceedings of 43nd IEEE Conference on Decision
and Control, pp. 3919-3924, invited paper, December 2004.
95 [CDC05zh].
Zongwu Zhu
and
Floyd B. Hanson,
"
A Monte-Carlo Option-Pricing Algorithm for Log-Uniform Jump-Diffusion
Model
,
Proceedings of Joint 44nd IEEE Conference on Decision
and Control and European Control Conference, pp. 1-6, 12 December
2005.
96 [ACC06].
Guoqing Yan
and
Floyd B. Hanson,
"
Option Pricing for a Stochastic-Volatility Jump-Diffusion Model with
Log-Uniform Jump-Amplitudes,"
Proceedings of American Control Conference, pp. 2989-2994,
14 June 2006.
97 [Sethi06]
Zongwu Zhu and Floyd B. Hanson,
"
Optimal Portfolio Application with Double-Uniform Jump
Model,"
Stochastic Processes, Optimization, and Control Theory:Applications
in Financial Engineering, Queueing Networks
and Manufacturing Systems/A Volume in Honor of Suresh Sethi,
International Series in Operations Research & Management Sciences,
Vol. 94, H. Yan, G. Yin, Q. Zhang (Eds.), Springer Verlag, New York,
pp. 331-358, Invited chapter, June 2006.
99 [ACC07].
Floyd B. Hanson
and
Guoqing Yan,
"
American Put Option Pricing for Stochastic-Volatility, Jump-Diffusion
Models,"
Proceedings of 2007 American Control Conference, pp. 384-389,
11 September 2007; in invited
WeA12.1: Stochastic Theory and Control in Finance I session.
100 [SIAMbook].
Floyd B. Hanson,
Applied Stochastic Processes and Control for Jump-Diffusions:
Modeling, Analysis and Computation,
SIAM Books: Advances in Design and Control Series,
published 03 October 2007.
WORK SUBMITTED OR NEARLY SUBMITTED
104 [IISC07].
Floyd B. Hanson,
"Stochastic Processes and Control for
Jump-Diffusions,"
under revision, 44 pages,
22 October 2007.
105 [BFS08].
Floyd B. Hanson,
Optimal Portfolio Problem for Stochastic-Volatility,
Jump-Diffusion Models with Jump-Bankruptcy Condition:
Practical Theory and Computation,
Fifth World Congress of Bachelier Finance Society, 2008,
27 pages, revised 11 July 2008.
(
See this page for abstract and SSRN paper download.)
106 [SIAMCT11].
Floyd B. Hanson,
Stochastic-Volatility, Jump-Diffusion Optimal Portfolio Problem with
Jumps in Returns and Volatility
,
SIAM Conference on Control and Its Applications (CT11),
26 pages, to be presented in
Invited Session MS22 Stochastic Methods in Finance,
Baltimore, MD.
(
See this page for abstract and SSRN paper download.)
(And/Or Slides?)
107[MF05zh].
Zongwu Zhu
and
Floyd B. Hanson,
"
Risk-Neutral Option Pricing for Log-Uniform
Jump-Amplitude Jump-Diffusion Model
,"
under revision, pp. 1-44, 20 August 2005.
This material is based upon work supported by the National Science
Foundation under Grants Numbers 880699, 9102343, 9301107, 9626692, 9973231,
0207081 in the Computational Mathematics Program.
Any opinions, findings, and conclusions or recommendations expressed in
this material are those of the author(s) and do not necessarily reflect
the views of the National Science Foundation or other agency.
Supercomputing research support was provided by
San Diego Supercomputing Center NPACI Account UIL203,
National Center for Supercomputing Applications
Grant Numbers DCR860001N, DMS890009N, DMS900016N, DMS920003N,
DMS960002N;
Pittsburgh Supercomputing Center Grant Numbers DMS940001P and DMS9400011P;
Argonne National Laboratory's Advanced Computing Research Facility;
Los Alamos National Laboratory's Advanced Computing Laboratory
ACL-Accounts Z803835 and gwqfbh-d.
Email Comments or Questions to Professor Hanson
Back to the Hanson's CV Page?
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23 September 2003
Abstract:
The estimated parameters of the log-return density for
log-normal-diffusion, log-uniform jump process are found for an observed
financial market distribution. When the observed data is collected into
bins, it is shown that the appropriate parameter estimation method is
the
multinomial maximum likelihood estimation. This result is independent
of
the theoretical distribution, since it is only assumed that the observed
distribution is the simulation of independent, identically distributed
random variables. For the application to the theoretical jump-diffusion
distribution, the estimation procedure is constrained by forcing the
first two moments of the theoretical distribution to be the same as that
for observed market distribution. The Standard and Poor's 500 stock
index for the 1992-2001 decade is used as the observed market data.
Numerically, the classical Nelder-Mead and our own direct search method
are used to find the maximum likelihood estimation of the parameters.
The results and performance of these numerical methods are compared
along with the our older weighted least squares estimation method.
The results of the two numerical approximations for the multinomial
estimation methods were similar, but the weighted least squares results
are not as good. In the severe test on the third and fourth moment
measures, the multinomial based methods differed significantly from the
same measures on the observed data, but did much better than the normal
distribution based weighted least squares.
Abstract:
Previously, we have shown that the proper method for estimating
parameters from discrete, binned stock log returns is the multinomial
maximum likelihood estimation, and its performance is superior to the
method of least squares. Also, useful formulas have been derived for
the density for jump-diffusion Previously, we have shown that the proper
method for estimating parameters from discrete, binned stock log returns
is the multinomial maximum likelihood estimation, and its performance is
superior to the method of least squares. Also, useful formulas have been
derived for the density for jump-diffusion distributions. Numerically,
the parameter estimation can be a large scale nonlinear optimization,
but we have successfully implemented variants of multi-dimension
direct search methods. In this paper, three jump-diffusion models using
different jump-amplitude distributions are compared. These jump-amplitude
distributions are the normal, uniform and double-exponential distribution.
The parameters of all three models are fit to the Standard and Poor's 500
log-return market data, given the same first moment and second central
moments. Our main results are first that uniform jump distribution has
superior qualitative performance since it produces genuine fat tails
that are typical of market data, whereas the other two have exponentially
thin tails. Secondly, the uniform distribution is quantitatively better
overall as measured by the closeness of both the skewness and kurtosis
coefficients to the data, although the double-exponential is best on
skewness while worst on kurtosis. However, the log-normal model has a
big advantage in computational costs of parameter estimation compared
with the others, while the double-exponential is most costly due to
having one more model parameter to fit.
Abstract:
A reduced European call option pricing formula by risk-neutral
valuation is given. It is shown that the European call and put
options for jump-diffusion models are worth more than that for the
Black-Scholes (diffusion) model with the common parameters. Due to
the complexity of the jump-diffusion models, obtaining a closed option
pricing formula like that of Black-Scholes is not viable. Instead,
a Monte Carlo algorithm is used to compute European option prices.
Monte Carlo variance reduction techniques such as both antithetic and
control variates are used. The numerical results show that this is a
practical, efficient and easily implementable algorithm.
Abstract:
An alternative option pricing model is proposed, in which the stock
prices follow a diffusion model with square root stochastic volatility
and a jump model with log-uniformly distributed jump amplitudes in the
stock price process. The stochastic-volatility follows a square-root
and mean-reverting diffusion process. Fourier transforms are applied
to solve the problem for risk-neutral European option pricing under
this compound stochastic-volatility jump-diffusion (SVJD) process.
Characteristic formulas and their inverses simplified by integration along
better equivalent contours are given. The numerical implementation of
pricing formulas is accomplished by both fast Fourier transforms (FFTs)
and more highly accurate discrete Fourier transforms (DFTs) for verifying
results and for different output.
Abstract:
This paper treats jump-diffusion processes in continuous time,
with emphasis on the jump-amplitude distributions, developing more
appropriate models using parameter estimation for the market in one
phase and then applying the resulting model to a stochastic optimal
portfolio application in a second phase. The new developments are the
use of double-uniform jump-amplitude distributions and time-varying
market parameters, introducing more realism into the application model
-- a log-normal diffusion, log-double-uniform jump-amplitude model.
Although unlimited borrowing and short-selling play an important role
in pure diffusion models, it is shown that borrowing and shorting is
limited for jump-diffusions, but finite jump-amplitude models can
allow very large limits in contrast to infinite range models which
severely restrict the instant stock fraction to [0,1]. Among all the
time-dependent parameters modeled, it appears that the interest and
discount rate have the strongest effects.
Abstract:
The numerical treatment for the American put option pricing is
discussed for a stochastic-volatility, jump-diffusion (SVJD) model
with log-uniform jump amplitudes. Heston's (1993) mean reverting,
square-root stochastic volatility model is used along with our uniform
jump-amplitude model. However, computation is needed for nonlinear
and multidimensional terms with dependence on the combined stock and
volatility state space. A systematic finite difference formulation of the
American put integro-partial differential complementary problem (PIDCP)
is implemented using a successive over-relaxtion method projected on the
maximum payoff function. Interpolation is used to construct the smooth
transition to the payoff of the corresponding free boundary problem.
Also, a fast, but less accurate, heuristic quadratic approximation,
originally due to MacMillan (1986), is corrected and extended from
pure diffusion models. The fast and simple quadratic approximation is
compared with a more accurate PIDCP formulation. The simple quadratic
approximation is briefly compared with market data.
Abstract:
An applied compact introductory survey of
Markov stochastic processes
and control in continuous time is presented.
The presentation is in tutorial stages,
beginning with deterministic dynamical
systems for contrast and continuing on to
perturbing the deterministic model with diffusions using Wiener
processes.
Then jump perturbations are added using simple Poisson
processes constructing the theory of simple jump-diffusions.
Next, marked-jump-diffusions are treated
using compound Poisson processes to include
random marked jump-amplitudes in parallel with
the equivalent Poisson random measure formulation.
Otherwise, the approach is quite applied,
using basic principles with no abstractions
beyond Poisson random measure.
This treatment is suitable for those in classical applied mathematics,
physical sciences, quantitative finance and engineering,
but having trouble getting started with the abstract measure-theoretic
literature. The approach here
builds upon the treatment of continuous functions in the regular
calculus and associated ordinary differential equations by adding
non-smooth and jump discontinuities to the model.
Finally, the stochastic optimal control of marked-jump-diffusions
is developed, emphasizing the underlying assumptions.
The survey concludes with applications in biology and finance,
some of which are canonical, dimension reducible problems and
others are genuine nonlinear problems.
Abstract:
This paper treats the risk-averse optimal portfolio problem
with consumption in continuous time with a stochastic-volatility,
jump-diffusion (SVJD) model of the underlying risky asset and the
volatility.
The new developments are the use of the SVJD model with
double-uniform jump-amplitude distributions and
time-varying market parameters for the optimal portfolio problem.
Although unlimited borrowing and short-selling play an important
role in pure diffusion models, it is shown that borrowing and
short-selling are constrained for jump-diffusions.
Finite range jump-amplitude models can allow constraints to be very
large in contrast to infinite range models which severely
restrict the optimal instantaneous stock-fraction to [0,1].
The reasonable constraints in the optimal stock-fraction
due to jumps in the wealth argument for stochastic dynamic
programming jump integrals remove a singularity in the
stock-fraction due to vanishing volatility.
Main modifications for the usual constant relative risk aversion (CRRA)
power utility model are for handling the partial integro-differential
equation (PIDE) resulting from the additional variance independent
variable, instead of the ordinary integro-differential equation (OIDE)
found for the pure jump-diffusion model of the wealth process.
In addition to natural constraints due to jumps when enforcing
the positivity of wealth condition, other constraints are considered
for all practical purposes under finite market conditions.
Computational, result are presented for optimal portfolio values,
stock fraction and consumption policies.
Also, a computationally practical solution of Heston's (1993)
square-root-diffusion model for the underlying asset variance
is derived.
This shows that the non\-negativity of the variance
is preserved through the proper singular limit of a simple
perfect-square form.
An exact, non\-singular solution is found for a special combination of
the Heston stochastic volatility parameters.
Abstract:
This paper treats the risk-averse optimal portfolio problem
with consumption in continuous time for a stochastic-jump-volatility,
jump-diffusion (SJVJD) model of the underlying risky asset and the
volatility.
The new developments are the use of the SJVJD model with
double-uniform jump-amplitude distributions and
time-varying market parameters for the optimal portfolio problem.
Although unlimited borrowing and short-selling play an important
role in pure diffusion models, it is shown that borrowing and
short-selling are constrained for jump-diffusions.
Finite range jump-amplitude models can allow constraints to be very
large in contrast to infinite range models which severely
restrict the optimal instantaneous stock-fraction to [0,1].
The reasonable constraints in the optimal stock-fraction
due to jumps in the wealth argument for stochastic dynamic
programming jump integrals remove a singularity in the
stock-fraction due to vanishing volatility.
Main modifications for the usual constant relative risk aversion (CRRA)
power utility model are for handling the partial integro-differential
equation (PIDE) resulting from the additional variance independent
variable, instead of the ordinary integro-differential equation (OIDE)
found for the pure jump-diffusion model of the wealth process.
In addition to natural constraints due to jumps when enforcing
the positivity of wealth condition, other constraints are considered
for all practical purposes under finite market conditions.
Computational results are presented for optimal portfolio values,
stock fraction and consumption policies.
Abstract:
Reduced European call and put option formulas by risk-neutral valuation
are given. It is shown that the European call and put options for
log-uniform jump-amplitude jump-diffusion models are worth more than that for
the Black-Scholes (diffusion) model with the common parameters. Due to
the complexity of the jump-diffusion models, obtaining a closed option
pricing formula like that of Black-Scholes is not tractable. Instead,
a Monte Carlo algorithm is used to compute European option prices.
Monte Carlo variance reduction techniques such as both antithetic and
optimal control variates are used to accelerate the calculations by
allowing smaller sample sizes. The numerical results show that this is
a practical, efficient and easily implementable algorithm.
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